Traveling wavefronts of a prey–predator diffusion system with stage-structure and harvesting

AbstractFrom a biological point of view, we consider a prey–predator-type free diffusion fishery model with stage-structure and harvesting. First, we study the stability of the nonnegative constant equilibria. In particular, the effect of harvesting on the stability of equilibria is discussed and supported with numerical simulation. Then, employing the upper and lower solution method, we show that when the wave speed is large enough there exists a traveling wavefront connecting the zero solution to the positive equilibrium of the system. Numerical simulation is also carried out to illustrate the main result

Perron Theorem in the Monotone Iteration Method for Traveling Waves in Delayed Reaction-Diffusion Equations

In this paper we revisit the existence of traveling waves for delayed reaction diffusion equations by the monotone iteration method. We show that Perron Theorem on existence of bounded solution provides a rigorous and constructive framework to find traveling wave solutions of reaction diffusion systems with time delay. The method is tried out on two classical examples with delay: the predator-prey and Belousov-Zhabotinskii models.Comment: 17 pages. To appear in Journal of Differential Equation